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Create systems of linear equations with each possible number of solutions.?

Create systems of linear equations with each possible number of solutions.

y=x+3, y=-2x-2; y=x+4, y=x+4; y=2x-6, y=2x+3

Explain the equations, and if there is other ways to write them. Is

it possible for the equations to look completely different but the solution

set still be "infinitely many"?

1 Answer

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  • 8 years ago
    Favorite Answer

    y = x + 3

    y = -2x - 2

    The equations are both linear and the system is consistent, so there is exactly 1 solution.

    y = x + 4

    y = x + 4

    There is only 1 unique equation, and as such, there are infinitely many solutions.

    y = 2x - 6

    y = 2x + 3

    The equations are linear, but the system is inconsistent, so there are no solutions.

    It is possible for 2 equations to look different at first glance, yet still have infinitely many solutions. For example, y = x + 4 and 3y = 3x + 12 looks different, but they are essentially the same and will result in infinitely many solutions when put together.

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